Boost Interval Arithmetic

The design of the Boost interval arithmetic library. We present the design of the Boost interval arithmetic library, a C++ library designed to handle mathematical intervals efficiently and in a generic way. Interval computations are an essential tool for reliable computing. Increasingly a number of mathematical proofs have relied on global optimization problems solved using branch-and-bound algorithms with interval computations; it is therefore extremely important to have a mathematically correct implementation of interval arithmetic. Various implementations exist with diverse semantics. Our design is unique in that it uses policies to specify three independent variable behaviors: rounding, checking, and comparisons. As a result, with the proper policies, our interval library is able to emulate almost any of the specialized libraries available for interval arithmetic, without any loss of performance nor sacrificing the ease of use. This library is openly available at

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Abate, Alessandro; Bessa, Iury; Cordeiro, Lucas; David, Cristina; Kesseli, Pascal; Kroening, Daniel; Polgreen, Elizabeth: Automated formal synthesis of provably safe digital controllers for continuous plants (2020)
  2. Song, Yanzhi; Yang, Zhouwang; Liu, Yuan; Deng, Jiansong: Function representation based slicer for 3D printing (2018)
  3. Chattopadhyay, Amit; Vegter, Gert; Yap, Chee K.: Certified computation of planar Morse-Smale complexes (2017)
  4. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  5. Wechsung, Achim; Scott, Joseph K.; Watson, Harry A. J.; Barton, Paul I.: Reverse propagation of McCormick relaxations (2015)
  6. Goualard, Frédéric: How do you compute the midpoint of an interval? (2014)
  7. Misener, Ruth; Floudas, Christodoulos A.: A framework for globally optimizing mixed-integer signomial programs (2014)
  8. Misener, Ruth; Floudas, Christodoulos A.: ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations (2014)
  9. Lundell, Andreas; Skjäl, Anders; Westerlund, Tapio: A reformulation framework for global optimization (2013)
  10. Nehmeier, Marco: Interval arithmetic using expression templates, template meta programming and the upcoming C++ standard (2012)
  11. Spurek, P.; Tabor, Ja.: Numerical verification of condition for approximately midconvex functions (2012)
  12. Markót, Mihály Csaba; Schichl, Hermann: Comparison and automated selection of local optimization solvers for interval global optimization methods (2011)
  13. Boissonnat, Jean-Daniel (ed.); Teillaud, Monique (ed.): Effective computational geometry for curves and surfaces (2007)
  14. Brönnimann, Hervé; Melquiond, Guillaume; Pion, Sylvain: The design of the Boost interval arithmetic library (2006)
  15. Martel, Matthieu: An overview of semantics for the validation of numerical programs (2005)